The home side were strongest in the opening exchanges, Josh Ruffels surging into the Pools' danger zone and winning a succession of corners in the first few minutes.
Just two minutes later, a fine shot by Connolly from a narrow angle was turned aside by Scott Flinders for an Oxford corner.
A lull followed until about five minutes to go in the first half, when the Pools won five corners one after the other, the third attempt needing a good save from Clarke to tip it over the bar.
Meanwhile, Jack Barmby saw his shot palmed away by the U's keeper just before the break.
Four minutes after the restart, the Pools were let off as the referee waved away penalty appeals from the hosts after a Simon Walton challenge inside the box.
The 26-year-old was soon sent off midway through the second half for accruing two yellow cards, and Oxford capitalised on their 10-man opposition when David Hunt's free kick was met by the head of Connolly and flew into the net in the 78th minute.
The result sees Oxford United go five points clear of seventh-placed Plymouth Argyle in the League Two playoff places, while Hartlepool remain in 10th place.